Prove that X^n-1+X^n-2+........+X+1 is irreducible over Z iff n is prime.© BrainMass Inc. brainmass.com March 4, 2021, 7:32 pm ad1c9bdddf
Please see the attached file.
Prove that is irreducible over Z iff n is prime.
For n=2, we have f(x)=x+1, clearly is irreducible.
Now we suppose n>2. Since n given as prime, n must be odd ...
This provides an example of proving a polynomial is irreducible.